No. The federal education tax credit does not take money out of any federal, state, or local public school budget. No funding already allocated to public schools is redirected through this program.
Instead, you get to decide where up to $1,700 of your money goes, rather than giving that amount to the federal government for them to decide how to spend it. You can contribute it to a qualifying Scholarship Granting Organization, choose the school you want to support, and receive the same amount back as a credit against your federal taxes.
The federal program can support students in public, private, and religious schools. The Opportunity Fund for Jewish Education specifically supports eligible students attending or planning to attend Jewish day schools.